Γ-MRP: Physical Constraint Laws of the Biological Operating System — Five Constraints on a Single Dimensionless Number Derive Body, Senses, and Brain

Every living system is a network of impedance interfaces. At each interface, a single dimensionless number — the reflection coefficient Γ = (Z₂−Z₁) / (Z₂+Z₁) — determines how much energy passes through and how much is wasted. Starting from the characteristic impedance Z = ρc and the energy identity |Γ|² + |T|² = 1, we establish five physical constraint laws: C1 (Energy Minimisation): All biological structures converge toward Γ → 0 under survival pressure. C2 (Phase-Boundary Information): Every impedance interface automatically generates a reflection signal encoding the boundary's properties — information without computation. C3 (Geometric Dimension): At every boundary, a quarter-wave bridge with impedance Zₘatch = √ (Z₁·Z₂) must emerge. Topological branching is the spatial unfolding of iterated C3. C4 (Geometric Scaling / c-Tuning): Within a single physical domain, the system adjusts effective wave speed by altering geometry — fibre diameter, branching count, cross-section. C5 (Domain Escape / ρ-Tuning): When geometric scaling is exhausted, the system escapes to a new physical domain, resetting the material density ρ and restarting the C4 cycle. The complete framework operates as a bidirectional causal chain: bottom-up, ρ and c determine Z, which determines Γ and T; top-down, the survival pressure imposed by Γ forces the system to reshape its material structure and dimensionality. With no fitted parameters, these five constraints produce: • A bilateral brain as the minimum factorisation of Z = ρ × c into two independent processing pipelines — one for density (ρ, FDM) and one for wave speed (c, TDM) • Bilateral subcortical structures (left/right hippocampus, amygdala, PFC) as the necessary replication of this factorisation • A thalamic gate whose attentional selection is governed by energy-density peaks, not computational routing • Neural fibre diversity as the C4 toolkit for impedance tuning, and chemical encoding at synapses as the C5 escape from geometric limits • Binary impedance classification (P = density, C = geometry) showing that all five senses are physically identical: a ΔP=0, ΔC=1 transition — pure geometric compression from surface to channel • Clinical predictions — phantom limb pain, dementia as LIFO shutdown, PTSD as c-channel Γ-lock, aging as impedance overdraft — all verified against published data with zero free parameters The paper includes: empirical validation using acoustic impedance data (SAM measurements), a comprehensive tissue classification table mapping 16+ human tissues to binary (P, C) quadrants, and falsifiable predictions testable by current electrophysiology protocols. Keywords: Reflection coefficient, Impedance matching, Minimum Reflection Principle, Neural architecture, Bilateral brain, Binary impedance encoding, Sensory universality, Biophysics